Traditional Verse -- sometimes referred to as "closed forms"
Free Verse -- sometimes referred to as "open forms"
Continuous Form
Stanzaic Form
Fixed Form -- e.g. sonnet, limerick, sestina, villanelle, haiku, etc.
Narrative -- e.g., ballad
Lyric -- a brief subjective poem strongly marked by imagination, melody, and emotion, and creating a single, unified impression -- e.g., ode, elegy, sonnet, epigram, aphorism, limerick, sestina, villanelle, haiku
(Adapted from Charters/Charters, Literature and Its Writers, Compact Second Edition, Chapters 8-11, and A Handbook to Literature, 9th edition.)